You could cut the damaged area so that it has a flat outer surface. Then use epoxy or gorilla glue to affix (with pressure) a new piece of cork that you've also cut to have a matching flat surface. Make the grain in the same direction. After curing, use an exacto knife and sandpaper to create a proper shape, taper, etc for the cork.
Or .... assuming it's a hollow fiberglass rod, you could install an entire new cork grip if you want.
First cut thru the rod at the junction of the cork and reel seat and then remove all the old cork. Get a new grip of your choice, and ream it to fit the blank and glue in place. Get a nice one, cheap ones are junk.
Then get a section of a junk rod blank and cut it to make a "stent" that slips snugly inside your rod's hollow blank under both the cork and reel seat. Cut the piece approx 5" and epoxy half of it in one piece, let it cure then glue in the other. Make sure the reel seat aligns with your stripper guide.
Strength is not a an issue as there's not a lot of stress on blank at that location because your hand is holding the cork above the joint. Stents are used frequently to repair rods in high stress areas, also a spigot ferrule is basically just a stent that is affixed to one piece of a rod blank and inserted / removed in the other.
